Imaginary Numbers
by The TARDIS Thief
Summary: Just because he was 'wrong' doesn't mean he deserved to be left behind. (In which the Captain flirts, Rose disapproves of the bow tie, and the Doctor thinks he's cool. Others disagree.) AU Season 2 - 11th Doctor
1. Fisticuffs at Dawn

**Disclaimer: It's not plagiarism if I don't claim it's mine. **

_"Look at these people, these human beings. Consider their potential! From the day they arrive on the planet, blinking, step into the sun, there is more to see than can ever be seen, more to do than- no, hold on. Sorry, that's The Lion King. But the point still stands."_

_ - Tenth Doctor, The Christmas Invasion_

There was a new man in the Doctor's place. A man with floppy brown hair, green eyes, and a frankly ridiculous chin. Rose wasn't sure who he was, but it was clear, he wasn't the Doctor she knew.

"Who are you?" She edged closer to the door, hoping to be able to make a quick escape if he turned out to be a villain of some sort. The man didn't answer her though.

"Legs, yes got legs, that's good, I like legs, me. Arms, fingers, ooh, lots of fingers, ears, nose chin, blimey, what a chin, hair- I'm a girl!" Rose watched as he hurriedly checked his Adam's apple "No, not a girl, that's good. Not a ginger though." He turned and seemed to see Rose for the first time. "Rose Tyler! Off to Barcelona. Love Barcelona, me, planet of dogs without noses, brilliant place."

Rose stayed near the exit, and glared at him suspiciously. "Who are you and what have you done with the Doctor?"

He looked surprised. "I am the Doctor."

"No you're not. The Doctor - northern bloke, short hair, weird ears. What have you done to him?"

"I am him. Same man, different face. It's a way to sort of… cheat death that my people had."

"It can't be." Rose shook her head. "Not possible."

The man walked closer. "Rose Tyler. We met at the old store you used to work at, when the Nestene consciousness started controlling the dummies. You have a mum named Jackie, your dad died when you were little, and you have a boyfriend named Ricky."

"His name is Mickey." Maybe this man really was the Doctor. She wondered why he hadn't told her about this before.

"Now…Barcelona, right?"

Rose wasn't sure she was ready to go with this man anywhere. "Do you think you could take me back to my house? I haven't seen my mum or Mickey for a while."

The Doctor looked a little disappointed, but quickly brightened up. "Sure, yeah! The engines need to calibrate anyway."

{DW}

When Jackie and Mickey reached the TARDIS, they were surprised to find that Rose opened the door alone. Mickey was the first to speak. "Where's the Doctor?"

Rose stepped out on to the street. "He said that he was just going to change his clothes."

"I though he always wore the same thing though?" Mickey asked confusedly.

Rose looked uncomfortable. "Yeah…just to warn you, he's sort of…changed. "

"What do you mean, changed?"

"He calls it regeneration. He's the same person but with a new face." As she finished, a man wearing a tweed jacket, pants that were slightly too small and, oh god, a _bow tie. _

"Who are you supposed to be then?" Jackie leaned into his face. "And why are you traveling with the Doctor?"

"I am the Doctor. Same man, new face. Taking this one out for a test run."

"What's with the bow tie then?"

"I wear a bow tie now." He straightened the offending item. "Bow ties are cool." The other three looked at him incredulously. "Now. Do I hear Christmas carols?" Finally convinced that he was, in fact, the Doctor, all be it not the same Doctor, Jackie slapped him hard on the cheek. "Ow! What was that for?"

"It's been twelve months since Rose left. Twelve months!"

"The TARDIS engines must not have calibrated correctly…Sorry?" He looked sheepish. "I was trying for twelve days."

~DW~

Still looking angry, Jackie escorted the rest of them back to there flat, and was at least somewhat courteous to the new Doctor, though she did seem amused when he walked into a wall because 'It was a new body and the steering was still a bit off'. They sat down to a cup of tea, while the Doctor began looking through the cupboards. "Have you got any apples, Jackie? I like apples now."

"Yeah. In the fruit bowl on the counter." The Doctor took an apple, bit into it and immediately spit it back out.

"I hate apples. Apples are rubbish."

"I thought you said you liked apples?"

"New mouth, new rules."

"What about bananas?" Rose suggested.

"Probably wouldn't work. Everything tastes different, like eating after you've brushed your teeth. What about pears?" Pears didn't work, or bread and butter, or beans, or even pizza.

The Doctor stared, deredly He then opened the freezer. "I know what I need! Fish sticks….and custard!." The others stared at him bemusedly as he dipped the fish sticks into the custard, and ate them with relish.

"That's disgusting…" Jackie muttered

"No. S'brilliant. You should try some." He waved the fish in the air. "Hey! What's on telly?"

"Oh, the Guinevere space probe. It's supposed to land on Mars pretty soon." Jackie turned up the volume.

"That's Harriet Jones! She's Prime Minister now?" Rose wondered how that had happened.

"Yeah. Won a landslide majority. She's been brilliant. The 'Golden Age of Britain' they're calling it."

The Doctor stood up abruptly. "It's Christmas Eve, and we're all still inside! Let's go caroling."

~DW~

Rose, Jackie and Mickey eventually managed to convince the Doctor that maybe caroling was _not _the best idea, but they did agree to all go shopping. They were having a great time and were just reconvening after going to get presents. The Doctor turned up wearing a strange red hat that looked vaguely Middle-Eastern. "What is that thing on your head?" Rose said, accusingly.

"I wear a fez now. Fezzes are cool."

"No they are not." Jackie said as she grabbed the offending item from his head. "I will not walk around the city with someone with that thing on his head."

"Fine. Ruin all my fun." The Doctor hung back to walk with Mickey as Rose pointed out a band of trombone-playing Santas.

Suddenly, those same Santas started blowing flames at the quartet. The Doctor yelled "Run!" and pulled out his sonic screwdriver. He soniced the creatures until they started to smoke, then ran to catch up with the others.

They all went back to the flat, and watched as the Doctor soniced everything he could see.

"What were those things, Doctor?" Rose said as she started to wrap presents.

"Pilot fish," he answered distractedly, then lowered his sonic screwdriver. "Jackie, where did you get that Christmas tree?"

"Oh I dunno. I thought one of you got it."

"That is not good. That is really not good." The tree started to spin, rapidly, as the Doctor tried to sonic it. "Why won't you work?" He muttered, tapping the screwdriver against the table.

"Doctor! Hurry!" Rose yelled form the doorway.

"There we go" The sonic screwdriver began to work, and the tree started sparking and smoking. They all returned to the kitchen, and sat around the table. "Those are pilot fish. Little, unimportant things that follow bigger things around. They can sense the energy from my regeneration."

"What do we do about them?"

"They're not a problem. They're not very powerful. The real problem is what they're following."

"I don't get it." Micky looked confused.

"Pilot fish: little fish that swim along side big fish, feeding off them. That's what these things are. But if these are the pilot fish…"

"Then what are they following?" Mickey said, a look of comprehension dawning on his face.

"Rickey!" the Doctor exclaimed, clapping him on the back. "Not such an idiot anymore. So we've just got to find out what else is here…"

"How are we going to do that, though?" Rose asked, tilting her head to the side.

"Whatever it is, it's going to be big. Really big. So, if we turn this on…" He pointed his screwdriver at the television, which fitzed and spluttered for a minute before turning on. "What's happened to you?" the Doctor said, gently tapping the screwdriver.

"Don't you think it's a bit weird how much attention he pays to a screwdriver?" Jackie leaned over to talk to Rose.

Rose peered at the Doctor. "Yeah, maybe."

Suddenly Mickey pointed to the telly and yelled, "Look, Doctor!"

_Footage from the Genevieve space probe is being transmitted live now. Is this proof of extra-terrestrial life, or just a hoax? Find out more in a minute. _

_"_Doctor…Do you think that that thing is what we're looking for?"

"Yes, almost definitely. That's a Sycorax, a violent, Conquistador-ish race with a strong code of honor. If they actually are here, we should get to UNIT now!' He said, running to where the TARDIS was parked

They all piled into the TARDIS and watched as the Doctor raced around the console room, frantically pushing buttons and pulling levers.

"Redecorated?" Rose said, spinning around to look at the more open space, with orange walls, glass floors and two levels.

"Just changed the desktop theme." The Doctor pulled a final lever and the TARDIS started to make its customary noise. "Ahh…UNIT. The Unified Intelligence Taskforce. Used to have a friend that worked here. The Brigadier, we called him. Wonder if he's still along?" He threw open the door and stepped out to find a severe-looking blonde woman waiting for him.

"Hello. My name is Kate Stewart." She checked her clipboard. "You must be the Doctor, then?"

"The Doctor. Yes, that's me."

"Come along then, sir. They want you upstairs." She looked around at the others, who were just stepping out of the doors. "And bring your companions if you must."

As they walked down the hallway, the Doctor started to really look at the woman next to him. "Kate Stewart, was it?"

"Yes."

"Any relation to Brigadier Lethbridge-Stewart?"

"He's my father."

"How's he doing?"

"He retired recently, and is now in a nursing home." She turned to face him. "You should go see him, you know. He always makes us put out an extra scotch in case you come around."

"Maybe I will." They reached the end of the hallway and entered a large open space filled with military personel. Kate led them to the back, where Harriet Jones, the director of the Guinevere project and several other people in suits were gathered around a computer. As they got closer, they began to overhear the conversation.

"What's happened? It sounds like English now."

"I don't know. Nothing's changed." The Doctor pushed his way to the front and put his arms around two of the people in suits.

"Hello, UNIT! That would be me, or rather my ship. She's in your head, translating."

"Who are you?"

"I'm the Doctor! I used to work here, as a scientific advisor, in the seventies." Immediately the team stood up and started saluting. "Don't salute!"

He peered through the people: "Harriet Jones! So nice to see you again. Prime Minister, now, right? "

She nodded. "Doctor?"

"Yup, new face, new bow tie, brand new me!"

"How is that possible?"

Rose spoke up. "It's complicated."

"Anyway, so glad you could come. Have you seen what's happening?"

"No." He looked at the computer screen, where pictures of hundreds of thousands of people standing on the edges of high structures were showing up. "What is this?"

"About one third of the world's population, all poised to jump."

"Do you know why?"

"We're pretty sure it has something to do with the blue energy around their heads; we checked the records, and all the UNIT employees up their have A+ blood, but other than that, not a clue."

"Hm."

"We also got this message from the Sycorax." She pressed play on another computer screen.

"Surrender or they will die"

"What did you say back?"

"That this planet is armed and will not surrender."

"But then why haven't they died?" The Doctor muttered as he soniced the screen, then stood up. "We need to get up there. Do you have coordinates?"

"Yes, here." The Doctor scanned them, then ushered everybody into the TARDIS, and started pushing buttons, while the UNIT team looked around incredulously

"It's it's…bigger on the inside."

"Yep! Dimensionally transcendent, aren't you, gorgeous," He said as he stroked the console.

Of the UNIT members, the one with the translator, leaned over to Jackie. "Did he just call a spaceship 'Gorgeous'?"

"Probably," Jackie replied, "He was doing much the same thing with a screwdriver before."

~DW~

They stepped out into a large chamber filled with hundreds of the aliens, who they could now see were wearing masks. The Doctor stepped out onto the platform, closely followed by the rest of the group. "Hello, Sycorax! Nice place you've got here. A bit roomy, maybe, but each to there own."

He stepped forward "Now, I hear you have a plan to invade the Earth. Controlling all those people, threatening to make them jump off buildings. bit of a dirty trick, isn't it."

"The humans will surrender this planet or they will die." The Sycorax growled, reaching for his sword.

"Oh, but I don't think you can kill them. You're controlling them in some way, but they already said that they wouldn't surrender." He spun around, as if looking for something, then headed over to a stand with a large, pulsating button on top. "Aha! Looks like a control matrix of some sort. Let me guess, blood control?" He opened the bottom of the stand to confirm his results. "That makes sense. So it won't matter if I do this!" He pressed the top button, to the astonishment and outrage of the humans on board.

"You've killed them all!" exclaimed Harriet Jones.

"If you check, you'll see that nobody's died."

The Sycorax leader looked murderous. "We have allowed them to live."

"No, blood control can't kill someone. Human will to live is to strong. It's like hypnosis - you can make someone walk to the edge, but you can't make them jump."

"We can take this planet by force."

The Doctor stepped up so that his face was inches from the Sycorax. "You can try. This planet is under my protection."

"Why would you protect these people?"

"They're incredible, humans."

"They are weak."

"They're just getting started."

"How will you protect them? You're inconsiquential. A mere ape."

"I think you'll find that I'm not. Have you heard of the Time Lords?"

"They're a legend. A story for children, nothing more."

"The Time Lords were very very real, though they're all gone now. It's just me left."

"Who are you to claim to be a legend?"

"I'm the Doctor. The Oncoming Storm, the Destroyer of Worlds. And I have developed a fondness for this planet, and I'll protect it with my life."

"I am not scared of you, Doctor. We will not leave."

"How about a sword fight then? For the planet?"

"Of course." They backed away, the Sycorax reaching for his sword.

"Ah, swordfighting. Very medieval." The Doctor grabbed a sword form one of the other Sycorax. "Met King Arthur once. Nice bloke, bit of a hero complex. Helped him out a couple times, and he made me his chief wizard."

"Get on with it already!" The Sycorax leader began advancing with his sword. The fight lasted for several minutes, both parties being pretty well matched, until the Doctor was lying up against the ship with his hand cut off.

"Oi! You cut off my hand!"

"Do you surrender?"

"I'm lucky this happened within the first forty-eight hours of my regeneration cycle, or I might be permanently missing a hand. Now, though I can do this!" The gathered crowd watched as the missing hand miraculously grew back. "Much better. Shall we continue?"

They fought for another several minutes until it was the Doctor who held the other at swordpoint. "Do you surrender?"

"Kill me, Doctor. Spare me the shame."

"I have never been one to take a life unnecessarily, and this is no exception. Do you surrender?"

"I surrender." The Doctor let him up, and turned to walk away. The Sycorax started to rush him from behind. He didn't even look up, just soniced a button, which made the floor fall out from under the alien.

"You had your chance." He looked at the screwdriver critically "Still need a new screwdriver. Not sure what happened to this one."

They walked back into the main room, where the Doctor gave one final warning to the Sycorax before sending them on their way, and returning the rest of them to London. He left Harriet and the UNIT members back at Downing Street, then headed for Jackie's flat. When they got there, they watched the Sycorax ship depart in silence.

All of a sudden, five green lasers streaked through the sky and blew up the retreating craft. "What just happened?" Rose exclaimed in shock.

The Doctor, on the other hand, looked completely unsurprised. "Oh, Harriet…" he muttered, "What have you done?" Rose looked at him incredulously.

"Come on, elaborate."

"Torchwood. An extra-government force created to defend the Earth against alien attack, mostly by scavenging alien things. They could have done this themselves, but I would bet my bow tie that she was the one who gave the order."

"What are you going to do?"

"Jackie, do you have a phone?"

~DW~

"Harriet Jones."

"Doctor."

"Did you give the order?"

"I had too."

"They were retreating!"

"We had to protect Earth. Sometimes you aren't there."

"There are laws about this sort of thing, you know."

"They attacked us."

"No, no. They aren't allowed to invade a level five planet, which you are. I'll give you a way to contact the Shadow Proclamation."

"The Shadow Proclamation?"

"A sort of inter-planetary police force."

"Thank you, Doctor."

"Don't blow up anymore spaceships, please.

"We won't."

"This is your last chance." He hung up abruptly. "There, that's sorted."

They all stayed for Christmas dinner, the Doctor eating what Rose suspected was now his signature dish - fish sticks and custard, while the rest of them ate the slightly burned turkey that Jackie had been cooking before. After dinner the Doctor and Rose, after much protest, set out for the TARDIS.

"I do like the new decor, you know." Rose spun around on the top floor, looking around the open area. "Much…cheerier."

"As I told you before, it's just the desktop theme. I should change it more often. Now, Rose Tyler, anywhere in space and time…no…wait." He pugged some numbers into the console. "I bring life…"

"What's going on?"

"Come along, Tyler. We're going back for the Captain!"


	2. Interlude: The Captain's Return

**This is not a real chapter, and therefore is very short. This week was crazy for me. **

**Disclaimer: All characters, places and sentient transport devices do not belong to me. **

Jack Harkness was alive. He knew that that wasn't possible: he had been hit by a Dalek, there was no coming back from that, not ever. He hoped this wasn't the afterlife, he really didn't want to spend the rest of time on Satellite Five. He stretched, got up and looked for the doors. He wondered what had happened to Rose and the Doctor, and if they'd survived the Dalek fleet. Jack was about to leave the hallway, when he heard the familiar wheezing sound that signaled the Doctor's arrival.

Sure enough, the large blue police box slowly materialized in front of him, and a young man in tweed and a bow tie stepped out. "Hello, Captain!"

Jack stepped up so he was right in front of him, and let his eyes travel up and down the man's body. Despite the professorish clothes, the man was very pretty. "Hello yourself," he said flirtatiously.

"Now's not the time, Jack, into the box!" Jack stepped in to find Rose leaning over the top balcony of a new, spacious, console room. The man from before started pushing buttons and pulling levers. "I'm sorry, girl, I feel it too, but we can't just leave him behind."

"Who are you?" Jack looked at him again. "Not that I care, mind you."

To his surprise, it was Rose who answered. "He's the Doctor."

"No, he's not."

The man in the bow tie looked up. "Yup! That's me - how do you like the new face?"

"That's…not possible."

"I regenerated. I'm surprised you haven't heard of it, honestly." He looked at Jack. "I thought you were taught about the Time War."

"We were only taught the basics. Time Lords v. Daleks, threatened all time, don't do that sort of thing. I thought the rest was legend."

The 'Doctor' stepped closer to him "You're a 51st century Time Agent turned con-man who left the Agency after they wiped two years of your memory. Rose and I rescued you after your 'perfect con' released nanogenes into World War II London. You were using the alias of 'Captain Jack Harkness.'"

Jack visibly relaxed. "I must say, Doc, I really though I was a dead man there."

The Doctor looked up sharply. "You were, Jack. You were dead."

"But I'm here now I…I thought I was hit by a Dalek death ray. How could I possibly be alive?"

"Rose brought you back." Jack turned to look at her.

"Don't look at me, he hasn't explained this to me either." Rose stood up and walked down,"I'm as confused as you are as to how you could be alive."

"Come, on Rose, you just missed me." Jack wiggled his eyebrows, and she laughed.

"Jack." The Doctor snapped his fingers in front of Jack's face. "Concentrate. I'm trying to explain things here. What do you remember last?"

"Daleks, everywhere. I was shot." He shrugged. "Then I woke up, and you appeared."

"Good. I was on time. Was a bit worried about getting that wrong, honestly, could have left you there for ages," the Doctor said, walking back around the console.

"Are your driving skills that bad? I could do better with my Vortex Manipulator."

"That thing is a piece of junk."

"No it's not. You're just jealous because you keep having to replace pieces."

"The TARDIS is one of the most sophisticated pieces of technology that exists in the universe today."

"That's just because there aren't any others left."

Rose stepped between them. "Stop fighting, boys. Now, Doctor, you were going to explain what happened to Jack?"

"After we left, I sent Rose back to the TARDIS, which sent her home, but she wouldn't stay there. She opened the heart of the TARDIS and absorbed it, then came back here and turned the Daleks to dust. I thought that was all she did, but I thought about it, and I realized that she would never have left you behind."

He wasn't sure why the Doctor was being so nervous and shifty. "So? I'm alive now."

"There's one more thing. When you were brought back, you were brought back for good."

"What do you mean?"

"You can't die."

Jack let this sink in. "How can I not be _able _to die."

"You're a fixed point in time; there's nothing that can take you out of the time stream, You shouldn't be able to exist."

"Shouldn't be able to exist?"

"You've studied basic mathematics, right?

"Of course."

"You're like an imaginary number made real; something not possible at all that has just walked up and said hello. It feels…unsettling, too, and it's making the TARDIS a bit scared."

"Can I still stay on, then?"

"Of course. She'll warm up to you eventually, but in the mean time, I'm going to let her take us where she wants to." He made a face. "That's basically what she does anyway."


End file.
